Is there any standard for this, and a website (or websites) that publishes the data on the web?
There are obvious problems with blindly republishing arbitrary data from a public blockchain, of course.
Depending on how long you're willing to wait, you might be able to publish with as little as $0.00061 per byte: https://bitcoinfees.earn.com/
For reference, the text of the HN homepage (excluding HTML tags) is about 4KB so ~$2 if you're willing to wait, or up to ~$200 if you're in a hurry. I'm not sure if op_return transactions are typically priced the same as standard transactions though.